Complex Asymptote questions

[dmor]

Please help with this question:

The function below has how many asymptotes?

y=(8x^2-x+4)/(x^2-6x+5)

I know that the answer is three, but I'm not sure why

Thanks for yhour help

 

[galactus]

What makes the denominator equal to zero?. Those are vertical asymptotes.

Since the degree of the numerator and denominator are the same, the ratio of the respective leading coefficients is the horizontal asymptote. That is, the line
$\displaystyle y=\frac{a_{n}}{b_{n}}$ is the horizontal asymptote. Where $\displaystyle a_{n}$ is the leading coefficient of the numerator and $\displaystyle b_{n}$ is the leading coefficient of the denominator.